Finite Group Databasebeta

← C31×#13899 #21470658

Subgroups — C31×#13899 #21470658

Order 7936.

2690 conjugacy classes of subgroups.

The subgroup lattice has 794 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×D4×C31C211yesmaximal, characteristic
2C2×C31×#386C212yesmaximal
3C2×C31×#385C212yesmaximal, complemented
4C2×C31×#380C211yesmaximal, characteristic, complemented
5C22×C31×#95C211yesmaximal, characteristic, complemented
6C31×#1441C212yesmaximal, complemented
7C31×#1439C212yesmaximal, complemented
8C31×C4⋊#95C211yesmaximal, characteristic, complemented
9C31×#1434C211yesmaximal, characteristic, complemented
10C31×C22⋊#95C211yesmaximal, characteristic, complemented
11C31×C22⋊#95C211yesmaximal, characteristic, complemented
12C23×D4×C31C2211yescharacteristic
13C24×C4×C31C2212yes—
14C24×C4×C31C2211yescharacteristic
15C24×C4×C31C2211yescharacteristic
16C2×C4×D4×C31—28no—
17C2×C4×D4×C31C418yescomplemented
18C22×C4⋊C4×C31C2212yes—
19C22×C4⋊C4×C31C2212yes—
20C22×C4⋊C4×C31C2211yescharacteristic
21C22×C22⋊C4×C31C2212yes—
22C22×C22⋊C4×C31C2212yes—
23C22×C22⋊C4×C31C2212yes—
24C22×C22⋊C4×C31C2211yescharacteristic
25C22×C22⋊C4×C31C2211yescharacteristic
26C22×C42×C31C2211yescharacteristic
27C31×#386—28no—
28C31×#385—28no—
29C31×#380—24no—
30C2×C31×#95—24no—
31C2×C31×#95C2211yescharacteristic
32C2×C31×#95C2211yescharacteristic
33C2×C31×#95C2211yescharacteristic
34C2×C31×#95C2212yes—
35C2×C31×#95C2212yes—
36C2×C31×#95C2212yes—
37C2×C31×#95C2212yes—
38C2×C31×#95C2212yes—
39C2×C31×#95C2212yes—
40C2×C31×#95C2211yescharacteristic
41C25×C31C2311yescharacteristic
42C25×C31C2311yescharacteristic
43C22×D4×C31—24no—
44C22×D4×C31—24no—
45C22×D4×C31C2×C414yes—
46C22×D4×C31D414yes—
47C22×D4×C31Q814yes—
48C23×C4×C31—24no—
49C23×C4×C31—24no—
50C23×C4×C31—24no—
51C23×C4×C31—24no—
52C23×C4×C31—22no—
53C23×C4×C31—22no—
54C23×C4×C31—22no—
55C23×C4×C31—24no—
56C23×C4×C31—22no—
57C23×C4×C31—24no—
58C23×C4×C31—24no—
59C23×C4×C31—42no—
60C23×C4×C31—42no—
61C23×C4×C31—42no—
62C23×C4×C31—42no—
63C23×C4×C31C2×C414yes—
64C23×C4×C31C2×C414yescomplemented
65C23×C4×C31C2312yes—
66C23×C4×C31C2312yes—
67C23×C4×C31C2311yescharacteristic
68C23×C4×C31C2312yes—
69C23×C4×C31C2312yes—
70C23×C4×C31C2311yescharacteristic
71C23×C4×C31C2311yescharacteristic
72C23×C4×C31C2311yescharacteristic
73C23×C4×C31C2311yescharacteristic
74C4×D4×C31—232no—
75C2×C4⋊C4×C31—24no—
76C2×C4⋊C4×C31—24no—
77C2×C4⋊C4×C31—24no—
78C2×C4⋊C4×C31—24no—
79C2×C4⋊C4×C31—24no—
80C2×C4⋊C4×C31—42no—
81C2×C4⋊C4×C31—42no—
82C2×C4⋊C4×C31C2×C414yescomplemented
83C2×C22⋊C4×C31—24no—
84C2×C22⋊C4×C31—24no—
85C2×C22⋊C4×C31—24no—
86C2×C22⋊C4×C31—24no—
87C2×C22⋊C4×C31—24no—
88C2×C22⋊C4×C31—24no—
89C2×C22⋊C4×C31—24no—
90C2×C22⋊C4×C31—24no—
91C2×C22⋊C4×C31—42no—
92C2×C22⋊C4×C31—42no—
93C2×C22⋊C4×C31C2×C414yes—
94C2×C22⋊C4×C31C2×C414yescomplemented
95C2×C22⋊C4×C31D418yes—
96C2×C42×C31—24no—
97C2×C42×C31C2×C414yescomplemented
98C31×#95—24no—
99C31×#95—22no—
100C31×#95—22no—
101C31×#95—24no—
102C31×#95—24no—
103C31×#95—24no—
104C31×#95—24no—
105C31×#95—22no—
106C31×#95—42no—
107C31×#95D414yescomplemented
108C24×C31—21no—
109C24×C31—21no—
110C24×C31—22no—
111C24×C31—22no—
112C24×C31—21no—
113C24×C31—21no—
114C24×C31—21no—
115C24×C31—22no—
116C24×C31—22no—
117C24×C31—21no—
118C24×C31—22no—
119C24×C31—21no—
120C24×C31—22no—
121C24×C31—21no—
122C24×C31C22×C412yes—
123C24×C31C22×C412yes—
124C24×C31C2×D412yes—
125C24×C31C2×D414yes—
126C24×C31C2×D412yes—
127C24×C31C2×Q812yes—
128C24×C31C2×Q812yes—
129C24×C31#4114yes—
130C24×C31C2411yescharacteristic
131C2×D4×C31—28no—
132C2×D4×C31—28no—
133C2×D4×C31—216no—
134C2×D4×C31—216no—
135C2×D4×C31C4⋊C4116yescomplemented
136C22×C4×C31—22no—
137C22×C4×C31—22no—
138C22×C4×C31—21no—
139C22×C4×C31—22no—
140C22×C4×C31—21no—
141C22×C4×C31—22no—
142C22×C4×C31—21no—
143C22×C4×C31—22no—
144C22×C4×C31—22no—
145C22×C4×C31—21no—
146C22×C4×C31—216no—
147C22×C4×C31—28no—
148C22×C4×C31—21no—
149C22×C4×C31—22no—
150C22×C4×C31—22no—
151C22×C4×C31—22no—
152C22×C4×C31—22no—
153C22×C4×C31—22no—
154C22×C4×C31—22no—
155C22×C4×C31—21no—
156C22×C4×C31—22no—
157C22×C4×C31—22no—
158C22×C4×C31—22no—
159C22×C4×C31—22no—
160C22×C4×C31—22no—
161C22×C4×C31—22no—
162C22×C4×C31—22no—
163C22×C4×C31—22no—
164C22×C4×C31—28no—
165C22×C4×C31—28no—
166C22×C4×C31—28no—
167C22×C4×C31—22no—
168C22×C4×C31—22no—
169C22×C4×C31—22no—
170C22×C4×C31—22no—
171C22×C4×C31—22no—
172C22×C4×C31—22no—
173C22×C4×C31—22no—
174C22×C4×C31—22no—
175C22×C4×C31—22no—
176C22×C4×C31—22no—
177C22×C4×C31—22no—
178C22×C4×C31—22no—
179C22×C4×C31—22no—
180C22×C4×C31—22no—
181C22×C4×C31—44no—
182C22×C4×C31—44no—
183C22×C4×C31—48no—
184C22×C4×C31—48no—
185C22×C4×C31—48no—
186C22×C4×C31—48no—
187C22×C4×C31—48no—
188C22×C4×C31—48no—
189C22×C4×C31—48no—
190C22×C4×C31—48no—
191C22×C4×C31—48no—
192C22×C4×C31—48no—
193C22×C4×C31C22×C412yes—
194C22×C4×C31C22×C412yes—
195C22×C4×C31C22×C412yes—
196C22×C4×C31C22×C412yes—
197C22×C4×C31C22×C412yes—
198C22×C4×C31C2×D414yes—
199C22×C4×C31C2×D414yes—
200C22×C4×C31C2×D414yes—
201C22×C4×C31C2×D412yes—
202C22×C4×C31C2×D412yes—
203C22×C4×C31C2×Q812yes—
204C22×C4×C31#4114yes—
205C22×C4×C31#4112yes—
206C4⋊C4×C31—28no—
207C4⋊C4×C31—48no—
208C4⋊C4×C31—48no—
209C22⋊C4×C31—28no—
210C22⋊C4×C31—48no—
211C22⋊C4×C31—48no—
212C22⋊C4×C31—48no—
213C22⋊C4×C31C22⋊C4116yescomplemented
214C42×C31—28no—
215#13899C3111yesmaximal, characteristic, direct product factor, Sylow
216C23×C31—22no—
217C23×C31—22no—
218C23×C31—22no—
219C23×C31—22no—
220C23×C31—24no—
221C23×C31—24no—
222C23×C31—24no—
223C23×C31—24no—
224C23×C31—24no—
225C23×C31—22no—
226C23×C31—24no—
227C23×C31—24no—
228C23×C31—24no—
229C23×C31—24no—
230C23×C31—22no—
231C23×C31—22no—
232C23×C31—22no—
233C23×C31—24no—
234C23×C31—22no—
235C23×C31—22no—
236C23×C31—22no—
237C23×C31—22no—
238C23×C31—22no—
239C23×C31—22no—
240C23×C31—24no—
241C23×C31—24no—
242C23×C31—22no—
243C23×C31—24no—
244C23×C31—22no—
245C23×C31—22no—
246C23×C31—22no—
247C23×C31—24no—
248C23×C31—42no—
249C23×C31—42no—
250C23×C31—42no—
251C23×C31—42no—
252C23×C31—42no—
253C23×C31—42no—
254C23×C31—42no—
255C23×C31—42no—
256C23×C31C2×C22⋊C414yes—
257C23×C31C2×C4⋊C414yes—
258C23×C31C2×C4⋊C414yes—
259C23×C31#11714yes—
260C23×C31#12118yes—
261C23×C31C22⋊Q818yes—
262C23×C31C23×C411yescharacteristic
263C23×C31C22×D412yes—
264C23×C31C22×D411yescharacteristic
265C23×C31C22×D411yescharacteristic
266C23×C31C22×Q811yescharacteristic
267C23×C31C2×#4112yes—
268C23×C31C2×#4111yescharacteristic
269C23×C31C2×#4112yes—
270C23×C31H(5,𝔽2)12yes—
271C23×C31H(5,𝔽2)11yescharacteristic
272C23×C312−1+411yescharacteristic
273D4×C31—232no—
274C2×C4×C31—22no—
275C2×C4×C31—22no—
276C2×C4×C31—22no—
277C2×C4×C31—22no—
278C2×C4×C31—22no—
279C2×C4×C31—22no—
280C2×C4×C31—22no—
281C2×C4×C31—22no—
282C2×C4×C31—24no—
283C2×C4×C31—24no—
284C2×C4×C31—24no—
285C2×C4×C31—24no—
286C2×C4×C31—24no—
287C2×C4×C31—24no—
288C2×C4×C31—24no—
289C2×C4×C31—24no—
290C2×C4×C31—22no—
291C2×C4×C31—22no—
292C2×C4×C31—22no—
293C2×C4×C31—24no—
294C2×C4×C31—24no—
295C2×C4×C31—24no—
296C2×C4×C31—24no—
297C2×C4×C31—24no—
298C2×C4×C31—24no—
299C2×C4×C31—416no—
300C2×C4×C31—416no—
301C2×C4×C31—432no—
302C2×C4×C31—42no—
303C2×C4×C31—42no—
304C2×C4×C31—42no—
305C2×C4×C31—42no—
306C2×C4×C31—42no—
307C2×C4×C31—42no—
308C2×C4×C31—42no—
309C2×C4×C31—42no—
310C2×C4×C31—42no—
311C2×C4×C31—42no—
312C2×C4×C31—42no—
313C2×C4×C31—42no—
314C2×C4×C31—42no—
315C2×C4×C31—42no—
316C2×C4×C31—42no—
317C2×C4×C31—42no—
318C2×C4×C31—42no—
319C2×C4×C31—42no—
320C2×C4×C31—42no—
321C2×C4×C31—42no—
322C2×C4×C31—42no—
323C2×C4×C31—42no—
324C2×C4×C31—42no—
325C2×C4×C31—42no—
326C2×C4×C31C2×C22⋊C414yes—
327C2×C4×C31C2×C22⋊C414yes—
328C2×C4×C31C2×C4⋊C414yes—
329C2×C4×C31C4×D414yes—
330C22×C4×D4C2×C3111yescharacteristic
331C2×#386C2×C3112yes—
332C2×#385C2×C3112yescomplemented
333C2×#380C2×C3111yescharacteristic, complemented
334C22×#95C2×C3111yescharacteristic, complemented
335#1441C2×C3112yescomplemented
336#1439C2×C3112yescomplemented
337C4⋊#95C2×C3111yescharacteristic, complemented
338#1434C2×C3111yescharacteristic, complemented
339C22⋊#95C2×C3111yescharacteristic, complemented
340C22⋊#95C2×C3111yescharacteristic, complemented
341C22×C31—24no—
342C22×C31—24no—
343C22×C31—24no—
344C22×C31—24no—
345C22×C31—24no—
346C22×C31—28no—
347C22×C31—28no—
348C22×C31—28no—
349C22×C31—28no—
350C22×C31—24no—
351C22×C31—24no—
352C22×C31—24no—
353C22×C31—24no—
354C22×C31—42no—
355C22×C31—42no—
356C22×C31—42no—
357C22×C31—44no—
358C22×C31—44no—
359C22×C31—44no—
360C22×C31—44no—
361C22×C31—42no—
362C22×C31#38018yescomplemented
363C22×C31C22×C22⋊C411yescharacteristic
364C22×C31C22×C4⋊C411yescharacteristic
365C22×C31C2×#11711yescharacteristic
366C22×C31C2×C4×D411yescharacteristic
367C22×C31C4×#4111yescharacteristic
368C22×C31#51811yescharacteristic
369C22×C31#52011yescharacteristic
370C22×C31C2×#12112yes—
371C22×C31C2×C22⋊Q812yes—
372C22×C31#52512yes—
373C22×C31#52912yes—
374C22×C31#53812yes—
375C22×C31#53912yes—
376C22×C31D4212yes—
377C22×C31D4211yescharacteristic
378C22×C31#54612yes—
379C22×C31#54612yes—
380C22×C31#54612yes—
381C22×C31#54712yes—
382C22×C31#54711yescharacteristic
383C22×C31D4×Q811yescharacteristic
384C22×C31#55411yescharacteristic
385C22×C31#55412yes—
386C4×C31—24no—
387C4×C31—24no—
388C4×C31—24no—
389C4×C31—24no—
390C4×C31—42no—
391C4×C31—44no—
392C4×C31—44no—
393C4×C31—82no—
394C4×C31—82no—
395C23×D4C22×C3111yescharacteristic
396C24×C4C22×C3112yes—
397C24×C4C22×C3111yescharacteristic
398C24×C4C22×C3111yescharacteristic
399C2×C4×D4—28no—
400C2×C4×D4C4×C3118yescomplemented
401C22×C4⋊C4C22×C3112yes—
402C22×C4⋊C4C22×C3112yes—
403C22×C4⋊C4C22×C3111yescharacteristic
404C22×C22⋊C4C22×C3112yes—
405C22×C22⋊C4C22×C3112yes—
406C22×C22⋊C4C22×C3112yes—
407C22×C22⋊C4C22×C3111yescharacteristic
408C22×C22⋊C4C22×C3111yescharacteristic
409C22×C42C22×C3111yescharacteristic
410#386—28no—
411#385—28no—
412#380—24no—
413C2×#95—24no—
414C2×#95C22×C3111yescharacteristic
415C2×#95C22×C3111yescharacteristic
416C2×#95C22×C3111yescharacteristic
417C2×#95C22×C3112yes—
418C2×#95C22×C3112yes—
419C2×#95C22×C3112yes—
420C2×#95C22×C3112yes—
421C2×#95C22×C3112yes—
422C2×#95C22×C3112yes—
423C2×#95C22×C3111yescharacteristic
424C2×C31—28no—
425C2×C31—44no—
426C2×C31C2×#38011yescharacteristic
427C2×C31#229011yescharacteristic
428C2×C31#231811yescharacteristic
429C2×C31D4×C22⋊C411yescharacteristic
430C2×C31#233911yescharacteristic
431C2×C31D4×C4⋊C411yescharacteristic
432C2×C31#234911yescharacteristic
433C2×C31#242412yes—
434C2×C31#242512yes—
435C2×C31#244912yes—
436C2×C31#245012yes—
437C25C23×C3111yescharacteristic
438C25C23×C3111yescharacteristic
439C22×D4—24no—
440C22×D4—24no—
441C22×D4C2×C4×C3114yes—
442C22×D4D4×C3114yes—
443C22×D4Q8×C3114yes—
444C23×C4—24no—
445C23×C4—24no—
446C23×C4—24no—
447C23×C4—24no—
448C23×C4—22no—
449C23×C4—22no—
450C23×C4—22no—
451C23×C4—24no—
452C23×C4—22no—
453C23×C4—24no—
454C23×C4—24no—
455C23×C4—42no—
456C23×C4—42no—
457C23×C4—42no—
458C23×C4—42no—
459C23×C4C2×C4×C3114yes—
460C23×C4C2×C4×C3114yescomplemented
461C23×C4C23×C3112yes—
462C23×C4C23×C3112yes—
463C23×C4C23×C3111yescharacteristic
464C23×C4C23×C3112yes—
465C23×C4C23×C3112yes—
466C23×C4C23×C3111yescharacteristic
467C23×C4C23×C3111yescharacteristic
468C23×C4C23×C3111yescharacteristic
469C23×C4C23×C3111yescharacteristic
470C4×D4—232no—
471C2×C4⋊C4—24no—
472C2×C4⋊C4—24no—
473C2×C4⋊C4—24no—
474C2×C4⋊C4—24no—
475C2×C4⋊C4—24no—
476C2×C4⋊C4—42no—
477C2×C4⋊C4—42no—
478C2×C4⋊C4C2×C4×C3114yescomplemented
479C2×C22⋊C4—24no—
480C2×C22⋊C4—24no—
481C2×C22⋊C4—24no—
482C2×C22⋊C4—24no—
483C2×C22⋊C4—24no—
484C2×C22⋊C4—24no—
485C2×C22⋊C4—24no—
486C2×C22⋊C4—24no—
487C2×C22⋊C4—42no—
488C2×C22⋊C4—42no—
489C2×C22⋊C4C2×C4×C3114yes—
490C2×C22⋊C4C2×C4×C3114yescomplemented
491C2×C22⋊C4D4×C3118yes—
492C2×C42—24no—
493C2×C42C2×C4×C3114yescomplemented
494#95—24no—
495#95—22no—
496#95—22no—
497#95—24no—
498#95—24no—
499#95—24no—
500#95—24no—
501#95—22no—
502#95—42no—
503#95D4×C3114yescomplemented
504C31#1389911yescharacteristic, direct product factor, Sylow
505C24—21no—
506C24—21no—
507C24—22no—
508C24—22no—
509C24—21no—
510C24—21no—
511C24—21no—
512C24—22no—
513C24—22no—
514C24—21no—
515C24—22no—
516C24—21no—
517C24—22no—
518C24—21no—
519C24C22×C4×C3112yes—
520C24C22×C4×C3112yes—
521C24C2×D4×C3112yes—
522C24C2×D4×C3114yes—
523C24C2×D4×C3112yes—
524C24C2×Q8×C3112yes—
525C24C2×Q8×C3112yes—
526C24#41×C3114yes—
527C24C24×C3111yescharacteristic
528C2×D4—28no—
529C2×D4—28no—
530C2×D4—216no—
531C2×D4—216no—
532C2×D4C4⋊C4×C31116yescomplemented
533C22×C4—22no—
534C22×C4—22no—
535C22×C4—21no—
536C22×C4—22no—
537C22×C4—21no—
538C22×C4—22no—
539C22×C4—21no—
540C22×C4—22no—
541C22×C4—22no—
542C22×C4—21no—
543C22×C4—216no—
544C22×C4—28no—
545C22×C4—21no—
546C22×C4—22no—
547C22×C4—22no—
548C22×C4—22no—
549C22×C4—22no—
550C22×C4—22no—
551C22×C4—22no—
552C22×C4—21no—
553C22×C4—22no—
554C22×C4—22no—
555C22×C4—22no—
556C22×C4—22no—
557C22×C4—22no—
558C22×C4—22no—
559C22×C4—22no—
560C22×C4—22no—
561C22×C4—28no—
562C22×C4—28no—
563C22×C4—28no—
564C22×C4—22no—
565C22×C4—22no—
566C22×C4—22no—
567C22×C4—22no—
568C22×C4—22no—
569C22×C4—22no—
570C22×C4—22no—
571C22×C4—22no—
572C22×C4—22no—
573C22×C4—22no—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—22no—
578C22×C4—44no—
579C22×C4—44no—
580C22×C4—48no—
581C22×C4—48no—
582C22×C4—48no—
583C22×C4—48no—
584C22×C4—48no—
585C22×C4—48no—
586C22×C4—48no—
587C22×C4—48no—
588C22×C4—48no—
589C22×C4—48no—
590C22×C4C22×C4×C3112yes—
591C22×C4C22×C4×C3112yes—
592C22×C4C22×C4×C3112yes—
593C22×C4C22×C4×C3112yes—
594C22×C4C22×C4×C3112yes—
595C22×C4C2×D4×C3114yes—
596C22×C4C2×D4×C3114yes—
597C22×C4C2×D4×C3114yes—
598C22×C4C2×D4×C3112yes—
599C22×C4C2×D4×C3112yes—
600C22×C4C2×Q8×C3112yes—
601C22×C4#41×C3114yes—
602C22×C4#41×C3112yes—
603C4⋊C4—28no—
604C4⋊C4—48no—
605C4⋊C4—48no—
606C22⋊C4—28no—
607C22⋊C4—48no—
608C22⋊C4—48no—
609C22⋊C4—48no—
610C22⋊C4C22⋊C4×C31116yescomplemented
611C42—28no—
612C23—22no—
613C23—22no—
614C23—22no—
615C23—22no—
616C23—24no—
617C23—24no—
618C23—24no—
619C23—24no—
620C23—24no—
621C23—22no—
622C23—24no—
623C23—24no—
624C23—24no—
625C23—24no—
626C23—22no—
627C23—22no—
628C23—22no—
629C23—24no—
630C23—22no—
631C23—22no—
632C23—22no—
633C23—22no—
634C23—22no—
635C23—22no—
636C23—24no—
637C23—24no—
638C23—22no—
639C23—24no—
640C23—22no—
641C23—22no—
642C23—22no—
643C23—24no—
644C23—42no—
645C23—42no—
646C23—42no—
647C23—42no—
648C23—42no—
649C23—42no—
650C23—42no—
651C23—42no—
652C23C2×C22⋊C4×C3114yes—
653C23C2×C4⋊C4×C3114yes—
654C23C2×C4⋊C4×C3114yes—
655C23C31×#11714yes—
656C23C31×#12118yes—
657C23C31×C22⋊Q818yes—
658C23C23×C4×C3111yescharacteristic
659C23C22×D4×C3112yes—
660C23C22×D4×C3111yescharacteristic
661C23C22×D4×C3111yescharacteristic
662C23C22×Q8×C3111yescharacteristic
663C23C2×#41×C3112yes—
664C23C2×#41×C3111yescharacteristic
665C23C2×#41×C3112yes—
666C23C31×H(5,𝔽2)12yes—
667C23C31×H(5,𝔽2)11yescharacteristic
668C23C31×2−1+411yescharacteristic
669D4—232no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—24no—
679C2×C4—24no—
680C2×C4—24no—
681C2×C4—24no—
682C2×C4—24no—
683C2×C4—24no—
684C2×C4—24no—
685C2×C4—24no—
686C2×C4—22no—
687C2×C4—22no—
688C2×C4—22no—
689C2×C4—24no—
690C2×C4—24no—
691C2×C4—24no—
692C2×C4—24no—
693C2×C4—24no—
694C2×C4—24no—
695C2×C4—416no—
696C2×C4—416no—
697C2×C4—432no—
698C2×C4—42no—
699C2×C4—42no—
700C2×C4—42no—
701C2×C4—42no—
702C2×C4—42no—
703C2×C4—42no—
704C2×C4—42no—
705C2×C4—42no—
706C2×C4—42no—
707C2×C4—42no—
708C2×C4—42no—
709C2×C4—42no—
710C2×C4—42no—
711C2×C4—42no—
712C2×C4—42no—
713C2×C4—42no—
714C2×C4—42no—
715C2×C4—42no—
716C2×C4—42no—
717C2×C4—42no—
718C2×C4—42no—
719C2×C4—42no—
720C2×C4—42no—
721C2×C4—42no—
722C2×C4C2×C22⋊C4×C3114yes—
723C2×C4C2×C22⋊C4×C3114yes—
724C2×C4C2×C4⋊C4×C3114yes—
725C2×C4C4×D4×C3114yes—
726C22—24no—
727C22—24no—
728C22—24no—
729C22—24no—
730C22—24no—
731C22—28no—
732C22—28no—
733C22—28no—
734C22—28no—
735C22—24no—
736C22—24no—
737C22—24no—
738C22—24no—
739C22—42no—
740C22—42no—
741C22—42no—
742C22—44no—
743C22—44no—
744C22—44no—
745C22—44no—
746C22—42no—
747C22C31×#38018yescomplemented
748C22C22×C22⋊C4×C3111yescharacteristic
749C22C22×C4⋊C4×C3111yescharacteristic
750C22C2×C31×#11711yescharacteristic
751C22C2×C4×D4×C3111yescharacteristic
752C22C4×#41×C3111yescharacteristic
753C22C31×#51811yescharacteristic
754C22C31×#52011yescharacteristic
755C22C2×C31×#12112yes—
756C22C2×C31×C22⋊Q812yes—
757C22C31×#52512yes—
758C22C31×#52912yes—
759C22C31×#53812yes—
760C22C31×#53912yes—
761C22D42×C3112yes—
762C22D42×C3111yescharacteristic
763C22C31×#54612yes—
764C22C31×#54612yes—
765C22C31×#54612yes—
766C22C31×#54712yes—
767C22C31×#54711yescharacteristic
768C22D4×Q8×C3111yescharacteristic
769C22C31×#55411yescharacteristic
770C22C31×#55412yes—
771C4—24no—
772C4—24no—
773C4—24no—
774C4—24no—
775C4—42no—
776C4—44no—
777C4—44no—
778C4—82no—
779C4—82no—
780C2—28no—
781C2—44no—
782C2C2×C31×#38011yescharacteristic
783C2C31×#229011yescharacteristic
784C2C31×#231811yescharacteristic
785C2D4×C22⋊C4×C3111yescharacteristic
786C2C31×#233911yescharacteristic
787C2D4×C4⋊C4×C3111yescharacteristic
788C2C31×#234911yescharacteristic
789C2C31×#242412yes—
790C2C31×#242512yes—
791C2C31×#244912yes—
792C2C31×#245012yes—
subgroupG/H
center, socleC24×C31C24
commutatorC23C23×C4×C31
Frattini, cosocleC24C24×C31
prime radicalC23×D4×C31C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C31 ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
3. C2×C31×#385C2semidirect
4. C2×C31×#380C2semidirect
5. C22×C31×#95C2semidirect
6. C31×#1441C2semidirect
7. C31×#1439C2semidirect
8. C31×C4⋊#95C2semidirect
9. C31×#1434C2semidirect
10. C31×C22⋊#95C2semidirect
11. C31×C22⋊#95C2semidirect
17. C2×C4×D4×C31C4semidirect
64. C23×C4×C31C2×C4semidirect
82. C2×C4⋊C4×C31C2×C4semidirect
94. C2×C22⋊C4×C31C2×C4semidirect
97. C2×C42×C31C2×C4semidirect
107. C31×#95D4semidirect
135. C2×D4×C31C4⋊C4semidirect
213. C22⋊C4×C31C22⋊C4semidirect
215. #13899C31direct (N × H)
332. C2×#385C2×C31semidirect
333. C2×#380C2×C31semidirect
334. C22×#95C2×C31semidirect
335. #1441C2×C31semidirect
336. #1439C2×C31semidirect
337. C4⋊#95C2×C31semidirect
338. #1434C2×C31semidirect
339. C22⋊#95C2×C31semidirect
340. C22⋊#95C2×C31semidirect
362. C22×C31#380semidirect
400. C2×C4×D4C4×C31semidirect
460. C23×C4C2×C4×C31semidirect
478. C2×C4⋊C4C2×C4×C31semidirect
490. C2×C22⋊C4C2×C4×C31semidirect
493. C2×C42C2×C4×C31semidirect
503. #95D4×C31semidirect
504. C31#13899direct (N × H)
532. C2×D4C4⋊C4×C31semidirect
610. C22⋊C4C22⋊C4×C31semidirect
747. C22C31×#380semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C22×C4×D4×C312
C2×C31×#3862
C2×C31×#3852
C2×C31×#3802
C22×C31×#952
C31×#14412
C31×#14392
C31×C4⋊#952
C31×#14342
C31×C22⋊#952
#1389931